发表机构
Mathematical Institute, University of Oxford; C. N. Yang Institute for Theoretical Physics, Stony Brook University（牛津大学数学研究所; 石溪大学杨振宁理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对任意有限群的非阿贝尔曲面码，通过规范固定构造正交错误基，并设计电荷与通量转移电路，实现精确且确定性的错误恢复协议。
AI 中文摘要
我们研究了基于任意有限群 $G$ 的量子双 $D(G)$ 的非阿贝尔拓扑曲面码的精确恢复。我们确定了一个正交错误基，该基由群乘法和不可约表示算子组成。当错误支持在晶格或对偶晶格上的闭合环路上时，由于稳定子的存在，基中存在冗余。为解决此问题，我们引入了一种规范固定，从而在码空间上得到一个完备且正交的错误基。假设输入为预先确定的、中性的可纠正错误簇，我们构造了电荷和通量转移电路，将错误移动到辅助比特上，然后将其投影出去。这是一种精确且确定性的恢复协议，适用于任何有限群（特别是非阿贝尔群）$G$ 的曲面码。
英文摘要
We study exact recovery for non-Abelian topological surface codes based on the quantum double $D(G)$ of any finite group $G$. We determine an orthogonal error basis, that is comprised of group multiplication and irreducible representation operators. Whenever the errors are supported on closed loops on the lattice or dual lattice, there is a redundancy in the basis, due to stabilizers. To remedy this, we introduce a gauge-fixing that results in a complete and orthogonal error basis on the code space. Assuming as input predetermined, neutral correctable error clusters, we construct charge and flux transfer circuits that move the errors onto ancillas that then get projected out. This is an exact and deterministic recovery protocol, applicable to surface codes for any finite, in particular non-Abelian, group $G$.
Comments22 pages
